What is the derivative of u/(u^2+6) ?

The derivative of u/(u^2+6) is (-u^2+6)/((u^2+6)^2)

What is the first derivative of u/(u^2+6) ?

The first derivative of u/(u^2+6) is (-u^2+6)/((u^2+6)^2)

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derivative of

\frac{u}{u ^{2} + 6}

\frac{- u ^{2} + 6}{( u ^{2} + 6 ) ^{2}}

Solution steps

\frac{d}{d u} (\frac{u}{u ^{2} + 6})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d u}{d u} ( u ^{2} + 6 ) - \frac{d}{d u} ( u ^{2} + 6 ) u}{( u ^{2} + 6 ) ^{2}}

\frac{d u}{d u} = 1

\frac{d}{d u} (u^{2} + 6) = 2 u

= \frac{1 \cdot ( u ^{2} + 6 ) - 2 uu}{( u ^{2} + 6 ) ^{2}}

1 \cdot (u^{2} + 6) - 2 uu = - u^{2} + 6

= \frac{- u ^{2} + 6}{( u ^{2} + 6 ) ^{2}}

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What is the derivative of u/(u^2+6) ?
The derivative of u/(u^2+6) is (-u^2+6)/((u^2+6)^2)
What is the first derivative of u/(u^2+6) ?
The first derivative of u/(u^2+6) is (-u^2+6)/((u^2+6)^2)